3 Answers
3

It depends on the magazine. Many publications have submission guidelines, and you might check those for what anything required in the cover letter. I found an interesting variety of requests with a few minutes of googling.

Your cover letter should contain the length of your story, your publishing history and any other relevant information (e.g., if you send us a story about a medical disaster and you happen to be an emergency room nurse, mention that.).

Please keep [your cover letter] brief, though we do like to hear from people who read and like the magazine. We're not concerned about writing degrees or past publications, though, so don't be daunted if you don't have an MFA or much in the way of previously published work.

In short, make certain to read the submission guidelines. (Online and print requirements may differ, even within the same publication.) A manuscript in the wrong format is not going to be read quickly, if at all. I don't know if the tone of the cover letter matters or not, although if I were submitting to McSweeny's I'd spend more time on that letter.

Write just a letter/email and ask for permission to send them your story.

In this letter (like in every cover letter) you should describe your story and yourself shortly and you should put in there, why they should publish your story. Why is it fantastic? Why do people really want to read it? What's different from all these other boring 50 submissions they got?

Yeah, I know, the second one is harder than the first ...

Edit:
To be more specific about describing your story:

It's not about: "It's a crime story about incest."
It's about: "It's about a woman killing her ex-husband to conceal that she has married her own son."

Note that some markets (particularly short fiction) explicitly request in their submission guidelines that you not describe the story.
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AshDec 7 '10 at 11:06

@Ash: Really? What's that good for? If your short stories only has two or three pages, I could understand it. For longer stories they skip an opportunity to filter the submissions.
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John SmithersDec 7 '10 at 13:06

1

I don't know about other genres, but in Sci-fi/Fantasy, it seems like most publications only want queries on novellas or serials, and the entire manuscript for anything shorter.
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sjohnstonDec 7 '10 at 15:47

For magazine writing, it's not so much a "cover letter" you're sending but more of a pitch. This is important because you're not introducing yourself (even though you need to convince the editor that you're THE person to go with for the story), you're trying to sell the story. Hook the editor. Make the person so curious and unsatisfied they s/he must contact you to find out more.

Most magazine editors have told me they see your pitch as a writing sample - can I trust this person to execute?

Give them the gist of the story in the first 2-3 paragraphs. Then answer the question, "why should I care?"

Add what else is in your story (if you have already finished writing it, I'm not sure whether you should say this or not. Some editors say they don't mind. Others have told me they prefer an unfinished piece because editors love to dig their fingers in and shape the piece).
Wrap up with your credentials (like a website where they can find your clips). This doesn't necessarily mean your degrees or awards. But something like "I'm a science writer who has covered X and Y and has published in A and B."
Then why you should care/hire me. And that's it. Shorter is better, but use as many words as you need to nail it.